I built horn speakers with MDF and titebond 1 then clad another layer on the 1'x4' sidewalls with green glue. I troweled on a layer to each mating surface, pressed them firmly, and shot a few staples in the center and each corner. I masked off a 1 inch border on the edge of the mating surfaces with blue tape, trowelled on the green glue, then removed the mask.
The ringing of the MDF was very strongly damped. Maybe it would have been just as damped with gluing them together with epoxy? Who knows.
The speakers were used inside on the carpet for a year and no green glue ever crept to the edges. The edges were not sealed or glued with other glue. Green glue soaks liquid into the substrate then it gets very viscous. Adhesion holds it in the thin layer without creeping. The holding strength in an application like this is very strong, but it is not structural.